Ramanujans Place in the World of Mathematics Essays Providing a Comparative Study 2nd Edition by Krishnaswami Alladi ISBN 813220767X 9788132207672

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Product details:

ISBN 10: 813220767X

ISBN 13: 9788132207672

Author: Krishnaswami Alladi

Ramanujan’s Place in the World of Mathematics: Essays Providing a Comparative Study 2nd Edition: This book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians throughout the history whose life and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan s spectacular discoveries and remarkable life and of the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. In the book, some aspects of Ramanujan s contributions, such as his remarkable formulae for the number pi, his pathbreaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. Thus the book is an enlightening study of Ramanujan as a mathematician and a human being.”

 

Ramanujan’s Place in the World of Mathematics: Essays Providing a Comparative Study 2nd Edition Table of contents:

Part I: Ramanujan and Other Mathematical Luminaries

• Chapter 1: Ramanujan: An Estimation
  100 Percent Pure Talent
• Chapter 2: Ramanujan: The Second Century
  Mock Theta Functions
  Ramanujan’s Congruences
  Rogers-Ramanujan Identities
  Special Functions
  The Notebooks
  The Lost Notebook
  The Undying Magic
• Chapter 3: L.J. Rogers: A Contemporary of Ramanujan
  Man of Many Talents
  The Rogers-Ramanujan Identities
  The Hard Hexagon Model
  The Mechanism
  Anticipated Others
  Invariant Theory
  False Theta Functions
  Continuing Rediscovery
• Chapter 4: P.A. MacMahon: Ramanujan’s Distinguished Contemporary
  Military Career and India
  Contributions to Mathematics
  Connection with Ramanujan
  The Hardy-Ramanujan Formula
  The Ramanujan Congruences
  The Rogers-Ramanujan Identities
  A Parity Question
  MacMahon’s Stature
• Chapter 5: Fermat and Ramanujan: A Comparison
• Chapter 6: J.J. Sylvester: Ramanujan’s Illustrious Predecessor
  Foundation Laid by Euler
  Sylvester Before Johns Hopkins
  Sylvester at Johns Hopkins
  Connection with Ramanujan’s Work
• Chapter 7: Erdös and Ramanujan: Legends of Twentieth Century Mathematics
  Eternally on the Move
  The Erdös Number
  Awards
  Almost a Saint
  Inspired by Ramanujan
  Probabilistic Number Theory
  Partitions
  The Prime Number Theorem
  Interaction with Indian Mathematicians
  Chancellor’s Fellowship
  Visits to MATSCIENCE
  Visits to Florida
  The Ramanujan Centennial
  The Ramanujan Journal
• Chapter 8: C.G.J. Jacobi: Algorist par-excellence
  Education
  Elliptic and Theta Functions
  The Fundamenta Nova
  Hard Times
  Vast Contributions
  Comparisons
  Ramanujan’s Letter and Reactions
  Ramanujan’s Methods
  Modular Equations
  Immortality
• Chapter 9: Evariste Galois: Founder of Group Theory
  Life of Galois
  The Birth and Growth of Group Theory
  Group Theory Today
  Ramanujan and Radicals
  Conclusion
• Chapter 10: Leonhard Euler: Most Prolific Mathematician in History
  Early Life and Education
  Position at St. Petersburg
  Work in Berlin
  Return to St. Petersburg
  Final Years in St. Petersburg
  Perfect Numbers
  Euler’s Constant
  Preponderance of Primes
  Reciprocals of the Cubes
  Euler’s Function
  Fermat’s Last Theorem
  The Taxi-Cab Equation
  Euler’s Identity
  The Euler Characteristic
  The Euler Line
  Partitions
• Chapter 11: G.H. Hardy: Ramanujan’s Mentor
  Early Life and Education
  Cambridge Education
  Influential Papers and Books
  Ramanujan’s Letters
  The Hardy-Ramanujan Interaction
  Formula for Partitions
  Round Numbers
  Honours for Ramanujan
  Move to Oxford
  Return to Cambridge
  Honours for Hardy
  Eccentricities, Habits and Beliefs
  Estimation of Ramanujan
• Chapter 12: J.E. Littlewood: Ramanujan’s Contemporary and Hardy’s Collaborator
  Early Life and Education
  Arrival in Cambridge
  Collaboration with Hardy
  Connection with Ramanujan
  Honours and Recognitions
  Hardy’s Two Great Partnerships
• Chapter 13: Niels Henrik Abel: Norwegian Mathematical Genius
  Early Life
  Exposure to Mathematics
  Unsolvability of the General Quintic
  Ramanujan and Radicals
  Discovery of Elliptic Functions
  Ramanujan and Elliptic Functions
  Infinite Series
  Ramanujan’s Theory of Infinite Series
  The Paris Treatise
  Posthumous Recognition
  Recognition for Ramanujan
  The Abel Prize
  The Ramanujan Prize
  A Game of Youth
• Chapter 14: Issai Schur: Ramanujan’s German Contemporary
  Early Life and Contributions to Group Theory
  Professional Life in Berlin
  The Rogers-Ramanujan Identities
  Schur’s Partition Theorem and Implications
  A Sad End
  Geniuses in Their Own Way
• Chapter 15: Robert Rankin: Scottish Link with Ramanujan
  Boyhood Years and Schooling
  The Cambridge Years
  Under Hardy’s Influence
  World War II
  Back to Cambridge
  Illustrious Career in Glasgow
  Gaps Between Prime Numbers
  Ramanujan’s Tau Function
  Ramanujan’s Lost Notebook
  Two Historical Books on Ramanujan
  Two Visits to India
  Honours and Recognitions
  The Ramanujan Journal

Part II: Some Aspects of Ramanujan’s Mathematics

• Chapter 16: Ramanujan and Pi
  Early History
  Squaring the Circle
  Representations for Pi
  Elliptic and Theta Functions
  The AGM
  Ramanujan
  Why Calculate the Digits of Pi
  Ramanujan’s Ability
• Chapter 17: Ramanujan and Partitions
  Partitions
  The Hardy-Ramanujan Formula
  Ramanujan Congruences
  Rogers-Ramanujan Identities
  Mock Theta Functions
  Everlasting Beauty
• Chapter 18: Major Progress on a Problem of Ramanujan

Part III: Book Reviews

• Chapter 19: Genius Whom the Gods Loved – A Review of “Srinivasa Ramanujan: The Lost Notebook and Other Works”
• Chapter 20: The Discovery and Rediscovery of Mathematical Genius – A Review of “The Man Who Knew Infinity”
• Chapter 21: A Review of “Ramanujan: Letters and Commentary”
• Chapter 22: A Review of “Ramanujan: Essays and Surveys”
• Chapter 23: A Review of “Partition: A Play on Ramanujan”

Part IV: Preserving Ramanujan’s Legacy

• Chapter 24: The Ramanujan Journal: Its Conception, Need, and Place
  Conception and Evolution
  Aims and Scope
  Addendum Dated September 2012
• Chapter 25: A Pilgrimage to Ramanujan’s Hometown
  Ramanujan
  SASTRA University and Ramanujan’s Home
  Accommodation and Sightseeing
• Chapter 26: The First SASTRA Ramanujan Prizes
  Addendum, September 2012
• Chapter 27: Ramanujan’s Growing Influence

 

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